Statistics, definitions and calculations Flashcards
How do you work out sensitivity?
Number of true positives/ all those with disease.
How do you work out specificity?
Number of true negatives/ all those without disease.
How do you calculate the negative predictive value?
Number of true negatives/ all those that test negative.
How do you calculate positive predictive value?
Number of true positives/ all those that test positive.
How do you calculate the likelihood ratio for a positive result?
The chance that a test is positive if a patient has the disease/ the chance that the test is positive if the patient is well.
How do you calculate the likelihood ratio for a negative result?
The chance that a test is negative if a patient has the disease/ the chance that the test is negative if the patient is well.
The larger the positive likelihood ratio….
… the greater the chance that you have the disease is your test is positive.
The smaller the negative likelihood ratio…
… the lesser the chance that you have the disease if your result is negative.
How do you calculate the chances of having a disease after a test?
The chances of having the disease before the test x likelihood ratio.
What is a nomogram?
A way of relating the likelihood ratios to the pre and post test probabilities.
What does the vertical line on a forrest plot represent?
The line of null effect.
What does the horizontal axis on a forrest plot represent?
The statistic that the studies are profiled to show.
Where is the line of null effect placed on a forrest plot?
At the value where there is no association between an exposure and outcome or no difference between 2 interventions.
In which cases will the line of null effect be placed at 1?
For relative statistics such as an odds ratio or a relative risk as these have a null effect value of 1.
In which cases will the line of null effect be placed at 0?
For absolute statistics such as absolute risk, ARR or SMD (standardised mean difference) as the null difference value for these is 0.
What does each horizontal line put onto a forrest plot represent?
A separate study which is being analysed.
Each study result being represented on a forrest plot has 2 components to it, what are they?
1) A black square box.
2) A horizontal line.
What does each individual black square box represent on a forrest plot?
A point estimate of the study result and the size of the study.
The bigger the box, the more participants in the study.
What does each individual horizontal line on a forrest plot represent?
The 95% confidence intervals of the study.
Each end of the line represents the boundaries of the confidence intervals.
What does the term ‘95% confidence interval’ mean?
The range of values within which you can be 95% certain the true value lies.
What does it mean if the horizontal line of a study crosses the line of null effect?
This means that the null value lies within the confidence interval and hence could be the true value.
**Basically, any study which crosses the line of null effect does not illustrate a statistically significant result.
What is a basic rule of thumb linking the size of a study and the horizontal line of the study?
Often, the bigger the study, the smaller the horizontal line. This means that it is less likely that those studies will cross the line of null effect because the 95% confidence intervals should have a much smaller range.
What is potentially the most important factor to look at on a forest plot?
The diamond at the bottom of the results.
What does the black diamond on a forest plot represent?
The point estimate and confidence intervals when you combine and average all of the individual studies together.
1) What do the horizontal points of the diamond represent?
2) What do the vertical points of the diamond represent?
1) The 95% confidence intervals of the combined point estimate.
2) The point estimate of the averaged studies.
On a forest plot, what does the column n/N mean which is immediately to the left of the forest plot?
n = the number of patients or individuals which had the event/ outcome in that particular group.
N = the total number of people in that group.
What is meant by the term ‘subtotal’ on a forest plot?
Tells you the total number of people in the treatment and control groups across all individual studies.
Also shows the average statistic and 95% confidence interval.
In order to assess the consistency of the papers analysed and shown on a forest plot, what statistic is used?
I squared.
**The I-squared statistic gives you an idea of the heterogeneity of the studies.
What is the rule of thumb about the I-squared statistic and heterogeneity of papers in a systematic review?
You want I-squared to be <50% because anything higher means that the papers could be inconsistent due to a reason other than chance.
If a study shown on a forest plot contains the null value in its 95% confidence interval, what is this likely to mean with regards to the p value?
It is most likely to mean that the p value for that study is >0.05 and that the study result is not statistically significant.
What is relative risk?
The ratio of the probability of an event occurring in the exposed group versus the non-exposed group OR the probability of an event occurring in a treatment group versus in a placebo group.
What is the calculation for calculating relative risk?
(a/a+b)/(c/c+d)
How do you calculate relative risk reduction?
(event rate in control group - event rate in treatment group) / event rate in control group.
What is absolute risk reduction?
The difference in event rate between control group and treatment group.
How do you calculate absolute risk reduction?
Event rate in control group - event rate in treatment group.
**a/(a+b) - c/(c+d)
What is meant by number needed to treat?
The number of people you need to treat with a drug in order to prevent one bad thing happening.
How do you calculate number needed to treat?
1 / absolute risk reduction.
Name 3 types of data.
Interval
Ordinal
Nominal
Describe what is meant by each of the following types of data:
1) Interval
2) Ordinal
3) Nominal
1) Quantitative data. Can be discrete (where only certain values are possible; number of falls/ attendance) or continuous (where any value is possible; height/ weight)
2) Qualitative but ordered. There are more than 2 categories which have a logical order (e.g. satisfaction with service).
3) Qualitative multi-nominal data with more than 2 categories that are not ordered (e.g. marital status).
Describe normal distribution.
A continuous, symmetrical, uni-modal distribution described by a mathematical equation.
What is the point of inflection?
The place where 1 standard deviation ends.
What is derived data?
Data that undergoes conversion or analysis following initial collection.
Describe where the mean, mode and median values all lie in a normal distribution curve.
Mean, mode and median are all equal and lie at the peak of the curve.
In normal distribution, what do you expect to lie within 1 SD of the mean?
You expect 68% of observations to lie within this range.
In a normal distribution, what do you expect to lie within 2 SDs of the mean?
You expect 95% of observations to lie within this range.
What is a standard normal distribution?
This is a normal distribution with a mean of 0 and a standard deviation of 1.
Describe the mean, median and mode in a negative skew of data.
Mean < Median < Mode.
Describe the mean, median and mode in a positive skew of data.
Mode > Median > Mean.
Name 3 measures of dispersion.
SD
Interquartile range
Range
Name 3 measures of location.
Mean
Median
Mode
What is the difference between null and alternate hypotheses?
Null = state that there is no difference or no effect.
Alternate = state that there is a difference or that there is an effect.
What does it mean if the probability is:
1) 0?
2) 1?
1) Something is certain not to happen.
2) Something is certain to happen.
What does a p-value show?
The p-value shows the probability that a null hypothesis is true.
What is standard deviation?
Expresses variation of the data around a mean.
**Shows how spread out the data is in a distribution.
**Used when talking about distributions.
What does standard error show?
How good an estimate is. It is used to describe the precision in the sample mean.
**Used when talking about estimates found from a sample.
1) When should you quote standard error of the mean?
2) When should you quote standard deviation?
1) When we want to say how good our estimate of the mean measurement is.
2) When we want to say how widely scattered the measurements are.
How do you calculate standard error of the mean?
standard deviation / square root of sample size
When will the value for the standard error of the mean be smaller?
With a larger sample size.
How do you calculate the standard error of a proportion?
SQUARE ROOT of p x (1 - p) / n
What is a confidence interval?
A range of values that probably contain the population mean or proportion.
What are confidence limits?
Values that state the boundaries of the confidence interval.
What does it mean to have a 95% confidence interval?
That you are 95% certain that the true value for a population lies within this range.
How do you calculate a confidence interval?
(mean ± z score) x (standard deviation / square root of n)
**this calculation gives you the upper and lower confidence limits.
1) What is a z score?
2) What is the z score for a 95% confidence interval?
1) A number that corresponds to the percentage of confidence interval you want to calculate.
2) 1.960
If a confidence interval does not include the null hypothesis value, what can you deduce?
That the difference is significant.
If a confidence interval contains the null hypothesis value, what can you deduce?
That the difference is not significant.
What do hypothesis tests allow us to do?
Establish the likelihood that the association we are observing is genuine, or simply due to chance.
What happens as a p value becomes smaller?
There is an increased likelihood that the null hypothesis will be disproven.
What is the conventional threshold for statistical significance?
p = 0.05.
What does it mean if a p value is <0.05?
This means that it IS statistically significant.
**Indicates strong evidence against the null as there is a less than 5% chance that the null is correct.
**Means that the null can be rejected.
What does it mean if a p value is >0.05?
This means that it IS NOT statistically significant.
1) What is a type I error?
2) What is a type II error?
1) Incorrect rejection of the null (false positive).
2) Acceptance of a false null (false negative).
Define risk.
The probability that an event will occur during a specified time.
**number who get the thing or event/ total number of people
How do you calculate risk ratio/ relative risk?
Risk in exposed group / risk in unexposed group.
How do you calculate relative risk?
(number with disease in exposed group / total exposed) DIVIDED BY (number with disease in unexposed group / total unexposed).
1) What does a risk ratio of 1 imply?
2) What does a risk ratio <1 imply?
3) What does a risk ratio >1 imply?
1) No difference in risk between exposed and unexposed.
2) Exposure had a protective influence over outcome.
3) Exposure increased risk outcome.
How do you calculate odds?
probability that ‘x’ happens / probability that ‘x’ does not happen.
** (p x ‘x’) / 1 - (p x ‘x’)
How do you calculate an odds ratio?
Odds in exposed group / odds in unexposed group.
Define hazard.
The risk at any given time of reaching the endpoint outcome in a survival analysis.
What do hazard ratios look at?
The influence of an exposure on an outcome over time.
How do you calculate a hazard ratio?
Hazard in exposed group / hazard in unexposed group.
Define number needed to treat.
The number of patients that would need to receive an intervention in question in order to prevent one adverse event from occurring.
How do you calculate number needed to treat?
1 / ARR.
**ALWAYS round number needed to treat UP.
How do you calculate absolute risk reduction?
Event rate in control group - event rate in treatment group.
When are the terms sensitivity, specificity and likelihood ratios often used?
When referencing the effectiveness of a diagnostic tool.
1) Define sensitivity.
2) Define specificity.
1) The proportion of those with disease who are correctly identified by a test.
2) The proportion of those without disease who are correctly identified by a test.
What is the likelihood ratio for a positive result?
The chance of a true positive result versus that of a false positive.
What are predictive values influenced by?
The prevalence of a disease amongst those in the study.
**LRs are not influenced by the prevalence of disease.
How do you calculate sensitivity?
Number of true positives / all those with disease.
How do you calculate specificity?
Number of true negatives / all those without disease.
Define positive predictive value.
Chance of having the disease if your test is positive.
Define negative predictive value.
Chance of not having the disease if your test is negative.
How do you calculate the positive predictive value?
Number of true positives / all those who text positive.
How do you calculate the negative predictive value?
Number of true negatives / all those who test negative.
Describe the relationship between prevalence, NPV and PPV.
As prevalence rises, NPV falls and PPV rises.
1) The larger the LR+ …
2) The smaller the LR- …
1) … the greater chance you have the disease if your test is positive.
2) … the lesser the chance you have the disease if your test is negative.
What do tests with a high sensitivity do?
Correctly classify a high proportion of people who really have a disease.
What do tests with a high specificity do?
Correctly classify a high proportion of people who do not have a disease.
